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natta225 [31]
3 years ago
8

From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How many different committees ar

e possible if
(a) 2 of the men refuse to serve together?
(b) 2 of the women refuse to serve together?
(c) 1 man and 1 woman refuse to serve together?
Mathematics
1 answer:
murzikaleks [220]3 years ago
6 0

Answer:

(a) 896

(b) 1000

(c) 910

Step-by-step explanation:

Number of women = 8

Number of men = 6

A committee consisting of 3 men and 3 women is to be formed.

(a) 2 of the men refuse to serve together.

Number of men who don't want to serve together = 2

Remaining men = 4

Total ways = Both men who don't want to serve together are not selected + only one of them is selected.

^{8}C_{3}\cdot ^{4}C_{3}+^{8}C_{3}\cdot ^{4}C_{2}\cdot ^{2}C_{1}

896

(b) 2 of the women refuse to serve together.

Number of women who don't want to serve together = 2

Remaining men = 6

Total ways = Both women who don't want to serve together are not selected + only one of them is selected.

^{6}C_{3}\cdot ^{6}C_{3}+^{6}C_{3}\cdot ^{6}C_{2}\cdot ^{2}C_{1}

1000

(c)1 man and 1 woman refuse to serve together.

Ways = Total ways - Both man and woman are select who refuse the serve together

^{8}C_{3}\cdot ^{6}C_{3}-^{5}C_{2}\cdot ^{7}C_{2}

910

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